A traveling wave is a type of vibration where a mechanical disturbance (wave) propagates continuously along the circumference of a rotationally periodic (i.e., cyclically symmetric) component. The rotationally periodic component may be a rotatable or a stationary component. The propagation speed of the wave relative to the component is a characteristic of the frequency and the wavelength. The excitation source for the traveling wave can be from unsteady fluid dynamic forces on the component or from mechanical interaction of various components coupled to the component. A defining characteristic of a traveling wave is the existence of two natural frequencies (eigenvalues) equal in value with the corresponding mode shapes (eigenvectors) similar but shifted in phase. The term “mode shape” refers to the deflected shape of the component corresponding to a given natural frequency. The term “mode” is shorthand for “natural mode” and refers collectively to a particular eigenvalue and its eigenvector(s). Thus, a component responding to resonant excitation of a traveling wave vibrates at a certain natural frequency and attains a deflected shape forming a continuous wave around its circumference, propagating at a specific speed relative to the component.
For example, traveling wave vibration in turbomachinery rotors (an exemplary “rotationally periodic rotatable component”) commonly involve disc traveling wave responses. Traveling waves propagate within the disc independent of the rotational speed of the turbomachinery rotor and induce harmonic alternating stresses in both the disc and blades thereof. When the elastic deformations (deflection) are mainly in the disc, the deflecting modes are called disc modes. Disc modes are in contrast to blade modes where the disc deflections become small compared with those of the blades. For the conventional axi-symmetrical circular disc, many of the natural disc modes are, in theory, in pairs with identical frequencies and similar, spatially orthogonal mode shapes, each with n equi-spaced nodal diameters, n being an integer. Thus, the conventional rotationally periodic component has inherently many natural frequencies and associated mode shapes. In the case of a disc, the mode shapes have been described in terms of its nodal diameters (ND). The practical consequence of this is that, with traveling wave excitation at or near a natural frequency, the node lines are not fixed with respect to the disc but propagate around the disc at the characteristic wave speed. At no point during the vibration cycle is the complete disc quiescent. Consequently, as the disc vibrates, the undesirable harmonic alternating stresses are induced in the rotationally periodic component, parts thereof, and/or the turbomachine.
Hence, there is a need for components resistant to traveling wave vibration and methods for manufacturing the same. There is also a need for systematically reducing traveling wave vibration of rotationally periodic components.